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A Turning Point Theory for Difference Equations

Series:

Research Horizons Seminar

Wednesday, September 24, 2008 - 12:00

1 hour (actually 50 minutes)

Location:

Skiles 255

Speaker:

Jeff Geronimo

,

School of Mathematics, Georgia Tech

A Turning point is where solutions to differential equations change behavior from exponential to oscillatory. In this region approximate solutions given by the powerful WKB method break down. In a series of paper in the 30's and 40's Langer developed a transformation (the Langer transformation) that allows the development of good approximate solutions (in terms of Airy functions) in the region of the Turning point I will discuss a discrete analog of this transformation and show how it leads to nice asymptotic formulas for various orthogonal polynomials.